CRICOS Provider Code: 00113B PHENOMENOGRAPHY AS A RESEARCH METHODOLOGY SANDRA HERBERT SCHOOL OF EDUCATION

CRICOS Provider Code: 00113B

PHENOMENOGRAPHY AS A RESEARCH METHODOLOGY

SANDRA HERBERTSCHOOL OF EDUCATION


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THIS PRESENTATION•phenomenography•conceptions of rate as an example•data collection •analysis → categories → outcome space •Discussion•Other example if time permits


PHENOMENOGRAPHY

Research method adapted for mapping the qualitatively different ways in which people experience, conceptualise, perceive, and understand various aspects of, and phenomena in, the world around them

(Marton, 1986, p. 31)•aims to:

reveal categories of descriptiondelineated by dimensions of variationemerging from data & hence,structuring categories into outcome space


WHY PHENOMENOGRAPHY?

•demonstrated efficacy in a range of educational research including mathematics.

•focus on ideas expressed by the group of participants.–attempts to describe phenomenon as seen by

participants.

•variation in conceptions is expected.

•identify variation (categories of description).–diversity of students → range of variation

–structure categories into an outcome space


OUTCOME SPACE•structured set of categories of description

•one category likely to display “correct meaning, correct knowledge or correct understanding” (Webb, 1996)

–as accepted by community of practice

•other categories display less complete understanding

•individual may hold >1 conception.

•outcome space considered to be final result of phenomenographic investigation (Marton,1988).


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ANALYSIS

•each data source considered several times•categories of description

–groupings of meaning statements

•dimensions of variation–themes of expanding awareness

•emerged from data over many iterations•categories delineated in terms of dimensions


OVERVIEW OF PHENOMENOGRAPHIC STUDY


THIS PHENOMENOGRAPHIC STUDY

•Investigating conceptions of rate•Selection of sample:

– aim for maximum variation;

– 20 diverse Year 10 students.

•Conduct interviews:– phenomenographic video-recorded semi-structured interviews

– based on computer simulations, enabling exploration of constant &

variable rate in multiple representations

•Phenomenographic analysis of responses to reveal students’ conceptions


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DATA COLLECTION

Consistent presentation to ensure attention to same phenomenon


PHENOMENOGRAPHIC ANALYSIS OF THIS STUDY

•immersion in data. –each video repeatedly viewed. –gestures used to give insights into meaning of words

•pooling & grouping of meaningful responses from data into meaning statements.

•grouping of meaning statements into initial categories.

•formation of initial dimensions•final dimensions & categories developed over many iterations.

•categories structured into outcome space. – based on dimensions– probably hierarchical. –some categories more complex & complete.


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EVOLUTION OF CATEGORIES & DIMENSIONS

•interviews transcribed–checked against audio & video

•immersion in data •interpret gist of participants’ verbal & non-verbal communications

•set of meaning statements


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Interpretation•suggests understanding of rate involving constant change in one variable wrt unit change of another variable.

Transcript

it goes up three point two meters

every half a meter


Interpretation of Gestures•identified key differences in rate for the window •gestures communicate awareness that graph of curved section not the same rectangular section.

•constant rate results in linear graph

TranscriptR: what do you think the graph [of non-rectangle window] might look like? [long pause]S: I don’t think it would be a straight line [pause] because this window’s not square hmm I dunno because its up the top umm curved there [pause] umm a straight line means its always the same R: what’s always the same?S: the umm


MEANING STATEMENTS1. Students see rate, which may vary, as a quantitative relationship between

two quantities which may vary. 2. Students see rate, which may vary, as a qualitative relationship between two

quantities which may vary. 3. Students see rate as a single number measuring a constant relationship

between two quantities which may vary. 4. Students see rate as a two numbers representing a constant relationship

between two quantities which may vary. 5. Students see rate as a constant relationship between two quantities.6. Students see rate as a comparison between two quantities. 7. Students see rate as a relationship between two quantities.8. Students see rate as something to do with change. 9. Students see rate as speed. 10. Students see rate as something to do with time.11. Students see rate as something to do with fractions. 12. Students see rate as an amount. 13. Students see rate as the result of a formula calculation. 14. Students see rate as a single number measuring something at a particular

stage. 15. Students see rate as a word they’ve heard eg. birth rate, interest rate16. Students see rate as nothing at all.17. Students see rate as something to do with maths18. Students see rate as something to do with two quantities


GROUPING OF MEANING STATEMENTS

CATEGORIES

16. Students see rate as nothing at all.15. Students see rate as a word they’ve heard eg. birth rate,

interest rate, council rates.11. Students see rate as something to do with fractions. 17. Students see rate as something to do with maths

12. Students see rate as an amount. 13. Students see rate as the result of a formula calculation. 14. Students see rate as a single number measuring something at

a particular stage. 8. Students see rate as something to do with change.

9. Students see rate as speed. 10. Students see rate as something to do with time.

6. Students see rate as a comparison between two quantities. 18. Students see rate as something to do with two quantities7. Students see rate as a relationship between two quantities.

5. Students see rate as a constant relationship between two quantities.

4. Students see rate as a two numbers representing a constant relationship between two quantities which may vary.

3. Students see rate as a single number measuring a constant relationship between two quantities which may vary.

2. Students see rate, which may vary, as a qualitative relationship between two quantities which may vary.

1. Students see rate, which may vary, as a quantitative relationship between two quantities which may vary.


VERSION 1

•5 categories & 3 dimensions

•categories of description1. Rate is seen as abstract concept that can be applied to variety of contexts

( with sub- categories or >1 category?)2. Rate is seen as something to do with motion.3. Rate is seen as something to do with time but not motion OR is this motion

but not time?4. Rate is seen as a mathematical concept, but not even understood in

application to motion5. Rate is not seen

•dimensions of variation

1. Type of Rate: with attributes ‘constant’ & ‘variable’

2. Context: with attributes ‘speed’ & ‘not-speed’

3. Relationship: with attributes ‘qualitative’ & ‘quantitative’


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ITERATIVE PROCESS•consideration of structure of outcome space –least to most complex

•some categories more complex & complete than others –include aspects of awareness of earlier categories

•more detail in descriptions of categories–return to data –focus on how rate was experienced with less emphasis on what the participants did or said

–ask “Can these be grouped?” “Are there examples of things that students say/do which illustrate this category?”


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VERSION 5

•Dimensions of Variation •another 2 dimensions added

– Property attributed to rate: with attributes ‘quality’ & ‘quantity’

– Characteristics of property: with attributes ‘1-fixed’, ‘1-changing’, ‘2-changing’

•labels & attributes of other dimensions changed– Context became Related variables: with attributes

‘distance&time’ & ‘any pair’ – Type of rate & Relationship were combined in ‘nature of

relationship’ with attributes with attributes ‘qualitative’, ‘quantitative-constant’& ‘quantitative-variable’


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VERSION 5

1. Rate is experienced as a word2. Rate is experienced as the result of a formula

calculation3. Rate is experienced as a change in a quality4. Rate is experienced as a change in a single

quantity5. Rate is experienced as the relationship between

two changing quantities6. Rate is experienced as the relationship between

two changing quantities of distance and time i.e. speed

7. Rate is experienced as an unchanging numeric relationship between two changing quantities

8. Rate is experienced as a numeric relationship between two changing quantities

Categories


VERSION 9Dimensions of Variation 1. Focus on word ‘rate’2. Focus on variables3. Focus on relationship between variables4. Focus on nature of related variables

Categories Rate is experienced as :-

A. a word rating a qualityB. a word associated with a numeric valueC. the result of a formula calculation with little meaning D. a single quantity E. a relationship between two changing quantities F. a constant numeric relationship between two changing quantities G. a numeric relationship between two changing quantities of distance

and time i.e. speed H. a numeric relationship between any two changing quantities


RATE OUTCOME SPACE

Rate experienced as a word associated with something numeric

Rate experienced as constant numeric relationship b/w 2

changing quantities

Rate experienced as a single quantity

Rate experienced as numeric relationship b/w any 2 changing

quantities

Rate experienced as rating of a quality

Rate experienced as qualitative relationship b/w 2 changing

quantities

Rate experienced as speed

Rate experienced as formula calculation

EVENTUALLY!!


Categories of Description

Dimension Attribute A B C D E F G H

Word ‘rate’ Quality

Quantity

Variables One - fixed

One - changing

Two - changing

Relationship Qualitative

Quantitative constant

Quantitative variable

Nature of Distance & time

variables Any pair

STRUCTURED BY DIMENSIONS


Sandra [email protected]

ARTICLES UTILISING PHENOMENOGRAPHYHerbert, S. & Pierce, R. (2013). Gesture as data for a phenomenographic analysis of mathematical conceptions. International Journal of Educational Research, 60, 1 - 10.Herbert, S. & Pierce, R. (2012). Revealing educationally critical aspects of rate. Educational Studies in Mathematics. 81 (1), 85-101

Herbert, S. , Vale, C., Loong, E., Bragg, L. & Widjaja, W. (submitted). Developing a framework for primary teachers’ perceptions of Mathematical Reasoning. Educational Studies in Mathematics Herbert, S. & Lynch, J. (in progress). Teachers’ Perceptions of Classroom Animals: A Phenomenographic Study


OTHER EXAMPLES

•Teachers’ perceptions of mathematical reasoning - ESM

•Teachers’ perceptions of classroom animals – forthcoming

•Teachers’ responses to AC:Science –collecting data


MEANING STATEMENTS

expressing ideasdescribing actions giving reasons for actions justifying actionsprovingdiscriminating between choices - selectioncommunication to oneself - self talkevaluation of an argumentnot relevant to younger yearsmaking connectionsapplication of prior knowledgeabout learning curriculum contentsolving word problemsan indicator of mathematical abilityan important part of mathematics which needs improvementa series of logical steps

Teachers see mathematical reasoning as:

solving open-ended problemsneeding less structured lessonsjustifying to another person.part of every mathematics lessonmetacognitionlanguage necessary to reason withinference from evidencesimilar to reasoning in other curriculum areasdiscussing with another persondifferent from contentthinkinglooking for patternsgeneralising

Grouping of Meaning Statements Initial Categories


CATEGORIES AND OUTCOME SPACE BASED ON DIMENSIONS

Audience Purpose Presentation Type of reasoningSelf Recount Verbal Adaptive

Others Compare/ Contrast Symbolic Inductive Make choices Diagram/Written Deductive Explain Gesture (action) Inferential Argue step-by-step Articulate reasons Justify Hypothesise Generalise Prove Evaluate Connect


Structure of outcome space Categories of Description

Dimension Attribute/Value A B C D E F G

Audience Self

Others

Purpose Recount

Compare/Contrast

Make choices

Explain

Argue step-by-step

Articulate reasons

Justify

Hypothesise

Generalise

Prove

Evaluate

Connect

Presentation Verbal

Symbolic

Diagram/written

Gesture (action)

Type of Adaptive

Reasoning Inductive

Deductive

Inferential


OUTCOME SPACE OF PRIMARY TEACHERS' PERCEPTIONS OF MATHEMATICAL REASONING

Category Perception of mathematical reasoning

Category A Reasoning is perceived to be thinking.

Category B Reasoning is perceived to be communicating thinking

Category C Reasoning is perceived to be problem solving

Category D Reasoning is perceived to be validating thinking Category E Reasoning is perceived to be forming conjectures

Category F Reasoning is perceived to be using logical arguments for validating conjectures

Category G Reasoning is perceived to be connecting aspects of mathematics


MEANING STATEMENTS

• Classroom animals are seen to be an opportunity for science education• Classroom animals are seen to be an opportunity for humane education• Classroom animals are seen to be an opportunity for addressing inequity• Classroom animals are seen to be an inconvenience• Classroom animals are seen to be an ethical dilemma• Classroom animals are seen to be a media opportunity• Benefits of classroom animals are seen to be dependent on the type of

animal• Benefits of classroom animals are seen to be dependent on the teacher• Classroom animals are seen to involve a cost (emotional cost, time cost,

financial cost, space costs)• Classroom animals are seen as an opportunity for student social-emotional

development• Classroom animals are seen an opportunity for cross-curricular learning

and enquiry learning• Classroom animals are seen an opportunity for connections (between home

and school; in-class and out-of-class; and classroom and yard/other physical spaces/locations)

Classroom animals


DIMENSIONSCurriculum Social/emotional Cost Connections

science responding to disadvantage

inconvenience wider community

humane ethical financial home

other personal development

space out of class

motivation emotional cross curricula


OUTCOME SPACE OF PRIMARY TEACHERS' PERCEPTIONS OF CLASSROOM ANIMALS

Category Perception of classroom animals

Category A Classroom animals are perceived to be valuable for science education.

Category B Classroom animals are perceived to be valuable for humane education.

Category C Classroom animals are perceived as an opportunity for cross curriculum learning

Category D Classroom animals are perceived to be an added burden in the classroom

Category E Classroom animals are perceived to provide opportunities for links to outside the classroom



Example: Lee and Gerber (1999) a study of Hong Kong school students’ perceptions of graphs, charts and maps

Outcome space consists of a set of 5 categories of description

Ordering of categories from least to most complexLearning – moving from a category to higher category

Category 1 Graphics are seen as ordinary drawings

Category 2 Graphics are seen as partially interpreted macro representations

Category 3 Graphics are seen as portraying localised patterns

Category 4 Graphics are seen as representing spatial relationships

Category 5 Graphics are seen as providing the basis for reflection, extrapolation and prediction


EXAMPLE: COPE (2002) A STUDY OF IT STUDENTS’ CONCEPTIONS OF INFORMATION SYSTEMSOUTCOME SPACE CONSISTS OF A SET OF 6 CATEGORIES OF DESCRIPTION ORDERED FROM MOST TO LEAST COMPLEX

Category 6 A number of communicating information systems within a single organisation

Category 5 A computerised data manipulation system and all the people and the data-related procedures they perform to support a single organisational function.

Category 4 A computerised data manipulation system supporting many people within a single organisational function.

Category 3 A data manipulation system supporting an individual within a single organisational function.

Category 2 A simple information retrieval system.

Category 1 A personal search of a static informationsource


SIMULATIONS WITH GSP

•enable exploration of constant & variable rate in multiple representations


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GEOMETERS’ SKETCHPAD


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SIMULATIONS WITH JMW

Documents

CRICOS Provider Code: 00113B PHENOMENOGRAPHY AS A RESEARCH METHODOLOGY SANDRA HERBERT SCHOOL OF EDUCATION